%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Solution to Homework 3, problem 2.
%  Solve the linear system Au=b where A is 
%  1.  an adaptive  finite element approximation to
%       -u_{xx} - u_{yy} = f(x,y)
%      in a circle with a slit cut from it
%      (generated by slit2.m)
%  or
%  2.  a uniform finite difference approximation to
%       - u_{xx} - u_{yy} -u_{zz} = f(x,y,z)
%      for (x,y,z) in (0,1) x (0,1) x (0,1),
%      with u = 0 on the boundary of the box.
%
%  Use varying meshes,  with h=1/(n+1), and solve using
%  various direct and iterative algorithms, recording
%  the resources consumed.
%
%  Plot the time and memory required by the various
%  solution algorithms.
%
%  problem2.m Dianne O'Leary  04-2005
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


disp('Generating some test problems')

[A1,b1,h1,A2,b2,h2] = slit2;
[A3,b3,h3] = laplace3d(25);

problems = ['Laplace equation on circle sector'
            'Laplace equation on circle sector'
            'Laplace equation on box,         '];
       
droptol = .05;

alg = ['                 Cholesky'
       'Cholesky, R-Cuthill-McKee'
       'Cholesky,  minimum degree'
       '     GMRES, restart =  20'
       '     GMRES, restart = 100'
       '     CG,       no precond'
       '     CG, diagonal precond'
       '     CG,  Cholinc precond'
       '     CG, mindeg + Cholinc'];

for i=1:3,
  if (i==1)
    A = A1; b = b1; h = h1;
  elseif (i==2)
    A = A2; b = b2; h = h2;
  else
    A = A3; b = b3; h = h3;
  end

  disp('  ')
  disp(sprintf('Solving %33s with n=%d and convergence tolerance = %5.2e', ...
             problems(i,:),length(b),.01*h^2))

  [nz,cflag,ctime,iter,rnorm] = runmethods(A,b,.01*h^2,droptol);

  disp('        Algorithm               storage     flag    time  iterations  residual_norm')
  for i=1:9,
    disp(sprintf('%25s      %8d %8d   %5.2e %5d       %5.2e', ...
            alg(i,:),nz(i),cflag(i),ctime(i),iter(i),rnorm(i)))
  end
end